Conjugate Duality for Constrained Vector Optimization in Abstract Convex Frame
Chaoli Yao, Shengjie Li · Numerical Functional Analysis and Optimization · 2019
This article focuses on a conjugate duality for a constrained vector optimization in the framework of abstract convexity. With the aid of the extension for the notion of infimum to the vector space, a set-valued topical function and the corresponding conjugate map, subdifferentials are presented. Following this, a conjugate dual problem is proposed via this conjugate map. Then, inspired by some ideas in the image space analysis, some equivalent characterizations of the zero duality gap are established by virtue of the subdifferentials.